Inequalities in Triangles

6-4 Inequalities in One Triangle

If one side of a triangle is longer than a second side, then the angle opposite the first side is larger than the angle opposite the second side.

Theorem 6-2

Answers: smallest is Z; largest is Y

If one angle of a triangle is larger than a second angle, then the side opposite the first angle is longer than the side opposite the second angle.

Name the longest side and the shortest side.

Theorem 6-3

Answers: longest; shortest is

Corollary 1◦ The perpendicular segment from a point to a line

is the shortest segment from the point to the line.

Corollary 2◦ The perpendicular segment from a point to a

plane is the shortest segment from the point to the plane.

The sum of the lengths of any two sides of a triangle is greater than the length of the third side.

Is it possible for a triangle to have sides with lengths 9, 6, and 2?

Two sides of a triangle have lengths 8 and 12. The length of the third side can be any number between _____ and _____.

Theorem 6-4 The Triangle Inequality

Answers: no; 4 and 20